Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8bz)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8bz.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, -(3/4)}, -z] == (1/(8121484800 z^(9/2))) (-2 Sqrt[z] (75983032125 - 16540524000 z - 972972000 z^2 + 798336000 z^3 - 401448960 z^4 + 589824000 z^5 + 63897600 z^6 + 1048576 z^7) Cos[2 Sqrt[z]] - 65536 Sqrt[Pi] z^(25/4) (157905 + 15840 z + 256 z^2) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + (75983032125 - 117851233500 z - 5935129200 z^2 - 2315174400 z^3 + 1064448000 z^4 - 778567680 z^5 + 5080350720 z^6 + 517472256 z^7 + 8388608 z^8) Sin[2 Sqrt[z]])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]